I am personally a big proponent behind the idea of the Creative Commons movement, which tries to create a free-er multimedia society where listeners, users and remixers build upon original works and freely exchange that information. The Creative Commons culture features the biggest amount of free music (22,000+ high quality albums), it's easy to find, and they usually have the right license for the job (ported to the legal systems of most countries). In other words, it's your best bet to find a music piece that will fit your video without potential legal consequences.

But first, you must get familiar with the 4 major Creative Commons clauses. Please note, the following is not legal advice as I am not a lawyer, but rather my own understanding of all things CC after having researched it for my own projects the last few years.

1. CC-ND (Creative Commons non-derivative)
When this "ND" clause is used, you can not use it on your video, because syncing audio and video is prohibited. This clause is the most restrictive of all, and it happens to govern a lot of the CC albums. It basically just allows for free personal viewing/listening and nothing else (unless you get permission from the copyright holder).

2. CC-NC (Creative Commons non-commercial)
Be very careful about this clause. Even if you are not charging money for your video, if you upload that video on a site that has advertisement in it (even if that's your own site that happens to have some ads, or YouTube, or Vimeo), then that’s commercial use and it's prohibited. However, if you only use it for your own web site that has no ads, or you burned DVDs, including burning for your friends and family, then it's fine.

3. CC-SA (Creative Commons share-alike) (and ArtLibre)
This clause allows usage of the composition as long as your video is licensed under the same license. This is not a bad deal, but it also means that if you have a great shot that Steven Spielberg wants to use as stock footage, he can't, because his movies won't be licensed under the same license (he will have to get written authorization directly from you to get around the "SA" clause). So this is a "viral" license: anything that uses music licensed as such, will have to use the same "SA" license from then on. Same goes for the popular French "ArtLibre" license (aka "Free Art License"). It might be what you need, or it might be not.

4. CC-BY (Creative Commons attribution)
Lastly, there is the "Attribution" clause. This is the most liberal for all the CC licenses, as it only asks to give credit to the artist, in the credit roll of your video. That's it, there are no other restrictions (apart from using the work for unethical purposes, but what constitutes as "unethical" is open to a public court's interpretation). That's what I personally use for my projects (check the credit rolls on my HD videos). Only problem with this is, from all the CC music available, only about 800+ albums are licensed only under the "BY" clause, so selection is limited. Although it should be enough. I found good music for my videos even at a time when only 45 such albums existed.

Here's a recent video of mine that uses CC-BY 3.0 music (most of my videos are also licensed under this very nonrestrictive license too), with the appropriate attribution in the credit roll:

Of course, most of the time there are combinations of these clauses (e.g. CC-BY-NC-ND, CC-BY-SA, CC-NC-SA etc etc), so pay attention when you download a piece of music. There are also some other types of clauses (e.g. CC with no clauses at all, Sampling+, etc), but very few compositions are licensed under these, so I won't be explaining them here.

Now, there are two major Creative Commons sources. ccMixter, and Jamendo.

- If you actually download from ccMixter, be very careful to not use compositions that remix upon commercial songs. For example, a potential ccMixter remix of Linkin Park's "Numb" song will be a violation of Linkin Park's copyright if you use it on your own video, even if the actual remix is licensed under a CC license. In other words: choose original compositions, and choose wisely! If you don't know if a composition is original and not RIAA-ridden, avoid. ccMixter personnel told me that they are very careful about such issues and so bumping into remixed music of... RIAA origins is not likely to happen.

- Jamendo's CC-BY-only URL is this. However, Jamendo doesn't let you search per license, so if you start searching or use the tags on their site, you will end up with search results that include all kinds of CC licenses. So be 100% sure, that the music you end up downloading and using has the right license. The license is written on the right side of each album page -- for example, the CC-BY clause is represented with a "little human" icon. If more icons are next to it, it means that the album is governed with more CC clauses, so you need to be careful. If you want to browse all major CC clauses on Jamendo instead of just CC-BY, here's the URL for it.

- If you really need to use a piece of music that it uses a more restrictive Creative Commons clause, you need to write to the author of the music and ask for permission. If this is a commercial project you are creating, you will need to actually get him to sign a contract.

- If your movie uses a free-er license than the music it is using (e.g. you license your movie under the CC-BY, but you use CC-NC-ND music under a signed contract), then you need to make this super-clear in the license of your movie. In some countries, you might need to use a less-free license for your movie, just because the music it contains is less free.

- Always make clear the license of your video on both the web page it appears and in its credit roll. If you don't show that the video is governed by a license, then by default, according to the US law, it will automatically be copyrighted and restricted (a'la MPAA/RIAA). Don't handcuff your creations. License them under a free license, like a Creative Commons one. Even if you pick the most restrictive CC license, do say so that you do. Allow others to build upon your work, this is how societies and culture evolve.

- The Creative Commons license just defines the kind of use that you authorize for your work. You still remain its author and keep all the rights. Regardless, if you pick CC-BY music or you specifically license other types of CC music, you can still license your video work under any other license.

- When you pick music that includes the CC "BY" clause in it, you need to give attribution to the musician. This is how you do this properly (unless there are specific instructions by the artist for what kind of attribution he/she wants), in your credit roll (in the web page that has the video, you can just mention that your video and/or the music is licensed under a particular CC clause without any additional info, but in the credit roll you need to give full credit):

Artist:[Name of the artist]Track Name:[Name of the music track used]Album Name:[Name of the music album track appears in]URL:[Jamendo or other URL where others can download the music]

This music track is licensed under the Creative Commons Attribution 3.0 license:
http://creativecommons.org/licenses/by/3.0/[you always include the URL of the license. Use the name and URL of the actual CC license the music is licensed under, in this example I just used the CC-BY]

[If your video is governed by the same license as the music track, just use this instead:]Music and video are licensed under the Creative Commons Attribution 3.0 license
http://creativecommons.org/licenses/by/3.0[...otherwise, just name the video license and include a URL for it, separately to the music's]

Video Copyright 2009[your name here]
[you don't say just "copyright", because this can cause problems with the music copyright legally-speaking]

Feel free to reword the above, but remember, all that info must be in the credit roll. You can find some ideas on how to "compact" all that info on my own Vimeo videos.

Finally, now that you have read all the above, please view this 19 minute video below, which is a talk of the Stanford university professor and co-founder of the Creative Commons movement, Larry Lessig. The talk is educating, entertaining, it explains the idea behind Creative Commons very well, and why it is important for our future generations for such-licensed work to exist. This is the talk that made me license all of my videos under one of the most liberal CC licenses, the CC-BY.